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A329323 Triangle read by rows: T(n,k) is the sum of the parts congruent to 0 mod k in the partitions of n into equal parts, 1 <= k <= n. 2

%I

%S 1,4,2,6,0,3,12,8,0,4,10,0,0,0,5,24,12,12,0,0,6,14,0,0,0,0,0,7,32,24,

%T 0,16,0,0,0,8,27,0,18,0,0,0,0,0,9,40,20,0,0,20,0,0,0,0,10,22,0,0,0,0,

%U 0,0,0,0,0,11,72,48,36,24,0,24,0,0,0,0,0,12,26,0,0,0,0,0,0,0,0,0,0,0,13,56,28,0,0

%N Triangle read by rows: T(n,k) is the sum of the parts congruent to 0 mod k in the partitions of n into equal parts, 1 <= k <= n.

%C Column k lists the terms of A038040 multiplied by k and interspersed with (k-1) zeros.

%F T(n,k) = A126988(n,k)*A134577(n,k).

%e Triangle begins:

%e 1;

%e 4, 2;

%e 6, 0, 3;

%e 12, 8, 0, 4;

%e 10, 0, 0, 0, 5;

%e 24, 12, 12, 0, 0, 6;

%e 14, 0, 0, 0, 0, 0, 7;

%e 32, 24, 0, 16, 0, 0, 0, 8;

%e 27, 0, 18, 0, 0, 0, 0, 0, 9;

%e 40, 20, 0, 0, 20, 0, 0, 0, 0, 10;

%e 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11;

%e 72, 48, 36, 24, 0, 24, 0, 0, 0, 0, 0, 12;

%e 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13;

%e 56, 28, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 14;

%e 60, 0, 30, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15;

%e 80, 64, 0, 48, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 16;

%e ...

%e For n = 6 the partitions of 6 into equal parts are [6], [3, 3], [2, 2, 2], [1, 1, 1, 1, 1, 1]. Then, for k = 2 the sum of the parts that are multiples of 2 is 6 + 2 + 2 + 2 = 12, so T(6,2) = 12.

%Y Column 1 is A038040.

%Y Row sums give A034718.

%Y Leading diagonal gives A000027.

%Y The number of positive terms in row n is A000005(n).

%Y Cf. A126988, A130540, A134577, A244051.

%K nonn,tabl

%O 1,2

%A _Omar E. Pol_, Nov 21 2019

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Last modified May 6 16:29 EDT 2021. Contains 343586 sequences. (Running on oeis4.)